Analysis of the magneto-rotational instability with the effect of cosmic-ray diffusion

TL;DR

This study investigates how cosmic-ray diffusion influences the magnetorotational instability (MRI) through linear stability analysis and MHD simulations, revealing that CR diffusion can enhance MRI growth rates depending on initial CR pressure distribution.

Contribution

It provides the first detailed analysis of the effects of cosmic-ray diffusion on MRI, considering different initial CR pressure distributions and models.

Findings

MRI growth rate is unaffected by CR diffusion with uniform initial CR pressure.

In non-uniform CR pressure distributions, higher CR diffusion increases MRI growth rate.

CR pressure gradients do not hinder matter movement driven by MRI.

Abstract

We present the results obtained from linear stability analysis and 2.5-dimensional magnetohydrodynamic (MHD) simulations of the magnetorotational instability (MRI), including the effects of cosmic rays (CRs). We took into account of the CR diffusion along the magnetic field but neglect the cross-field-line diffusion. Two models are considered in this paper: shearing box model and differentially rotating cylinder model. We studied how MRI is affected by the initial CR pressure (i.e., energy) distribution. In the shearing box model, the initial state is uniform distribution. Linear analysis shows that the growth rate of MRI does not depend on the value of CR diffusion coefficient. In the differentially rotating cylinder model, the initial state is a constant angular momentum polytropic disk threaded by weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both results are confirmed by MHD simulations. The MHD simulation results show that the outward movement of matter by the growth of MRI is not impeded by the CR pressure gradient, and the centrifugal force which acts to the concentrated matter becomes larger. Consequently, the growth rate of MRI is increased. On the other hand, if the initial CR pressure is uniform, then the growth rate of the MRI barely depends on the value of the CR diffusion coefficient.